Abstract

Partly of an expository nature, this article brings together a number of notions related to sufficiency in an abstract measure theoretic setting. The notion of a coherent statistical model, as introduced by Hasegawa and Perlman [6], is studied in some details. A few results are generalized and their earlier proofs simplified. Among other things, it is shown that a coherent model can be connected in the sense of Basu [2] if and only if no splitting set (Koehn and Thomas, [7])
exists.

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